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Simplifying (65 + -1x)(35 + -1x) = 100 Multiply (65 + -1x) * (35 + -1x) (65(35 + -1x) + -1x * (35 + -1x)) = 100 ((35 * 65 + -1x * 65) + -1x * (35 + -1x)) = 100 ((2275 + -65x) + -1x * (35 + -1x)) = 100 (2275 + -65x + (35 * -1x + -1x * -1x)) = 100 (2275 + -65x + (-35x + 1x2)) = 100 Combine like terms: -65x + -35x = -100x (2275 + -100x + 1x2) = 100 Solving 2275 + -100x + 1x2 = 100 Solving for variable 'x'. Reorder the terms: 2275 + -100 + -100x + 1x2 = 100 + -100 Combine like terms: 2275 + -100 = 2175 2175 + -100x + 1x2 = 100 + -100 Combine like terms: 100 + -100 = 0 2175 + -100x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2175' to each side of the equation. 2175 + -100x + -2175 + x2 = 0 + -2175 Reorder the terms: 2175 + -2175 + -100x + x2 = 0 + -2175 Combine like terms: 2175 + -2175 = 0 0 + -100x + x2 = 0 + -2175 -100x + x2 = 0 + -2175 Combine like terms: 0 + -2175 = -2175 -100x + x2 = -2175 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2175 + 2500 Reorder the terms: 2500 + -100x + x2 = -2175 + 2500 Combine like terms: -2175 + 2500 = 325 2500 + -100x + x2 = 325 Factor a perfect square on the left side: (x + -50)(x + -50) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + -50) equal to 18.027756377 and -18.027756377.Subproblem 1
x + -50 = 18.027756377 Simplifying x + -50 = 18.027756377 Reorder the terms: -50 + x = 18.027756377 Solving -50 + x = 18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 18.027756377 + 50 Combine like terms: -50 + 50 = 0 0 + x = 18.027756377 + 50 x = 18.027756377 + 50 Combine like terms: 18.027756377 + 50 = 68.027756377 x = 68.027756377 Simplifying x = 68.027756377Subproblem 2
x + -50 = -18.027756377 Simplifying x + -50 = -18.027756377 Reorder the terms: -50 + x = -18.027756377 Solving -50 + x = -18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -18.027756377 + 50 Combine like terms: -50 + 50 = 0 0 + x = -18.027756377 + 50 x = -18.027756377 + 50 Combine like terms: -18.027756377 + 50 = 31.972243623 x = 31.972243623 Simplifying x = 31.972243623Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.027756377, 31.972243623}
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